It was an open question for a long time if black holes obeyed the laws of thermodynamics. Everything else we know does, so we figured they should--it would be odd if they didn't. Hawking radiation gave a plausible mechanism that explains how they follow the laws of thermodynamics.

What's also nice about it is that (as I understand it) he didn't invent new physical laws, but rather applied quantum mechanics to what general relativity told us about black holes at the event horizon. So assuming GR and quantum mechanics are accurate theories, black holes don't break the laws of thermodynamics.